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CENTER OF MASS AND MOMENT OF INERTIA     141
or
similarly
and
2m.'
Sm
(10
Evidently x, y, and z are the coordinates of the center of mass.
ILLUSTRATIVE  EXAMPLES.
1.  Find the center of mass of two particles of masses m and nm, which are separated by a distance a.
Taking the origin of the axes at the particle which has the mass m, Fig. 72, and taking as the x-axis the line which joins the two particles we get
- _. Q + nma
m + nm
n
FIG. 72.
2.  Find the center of mass of three particles of masses m, 2 m, and 3 m, which are at the vertices of an equilateral triangle of sides a. Choosing the axes as shown in Fig. 73 we have - _ 0 + 2 ma + 3 ma cos 60
m + 2m + 3m = x72 a,
-- 0 + 0 + 3 ma sin 60 6m
2=0.